I have a problem that I've nearly finished but I'm stuck on the last bit so I'm hoping someone could help out. The question is
Evaluated on the region of between z=1 and z=2.
My workings so far are....
With z=√(x²+y²), the integrand should become
which simplifies to
Now I have
To evaluate using polar coordinates, I need to determine the limits of integration.
Since z ranges from 1 to 2 and the equation of the cone is z=r, I have , and
By substituting in x=r*cos(θ) and y=r*sin(θ), and multiplying by 'r' (the Jacobian determinant), I get
i think the best way is to integrate WRT r first:
(im going to leave out the for now)
I know I then simplify this and integrate WRT theta but this is where I'm running into difficulties so any help at all would be so great.